rf110_normintegration.py

# /
#
# 'BASIC FUNCTIONALITY' ROOT.RooFit tutorial macro #110
#
# Examples on normalization of p.d.f.s,
# integration of p.d.fs, construction
# of cumulative distribution functions from p.d.f.s
# in one dimension
#
# 07/2008 - Wouter Verkerke
#
# /

import ROOT


def rf110_normintegration():
    # S e t u p   m o d e l
    # ---------------------

    # Create observables x,y
    x = ROOT.RooRealVar("x", "x", -10, 10)

    # Create p.d.f. gaussx(x,-2,3)
    gx = ROOT.RooGaussian(
        "gx", "gx", x, ROOT.RooFit.RooConst(-2), ROOT.RooFit.RooConst(3))

    # R e t r i e v e   r a w  &   n o r m a l i z e d   v a l u e s   o f   R o o F i t   p . d . f . s
    # --------------------------------------------------------------------------------------------------

    # Return 'raw' unnormalized value of gx
    print "gx = ", gx.getVal()

    # Return value of gx normalized over x in range [-10,10]
    nset = ROOT.RooArgSet(x)
    print "gx_Norm[x] = ", gx.getVal(nset)

    # Create object representing integral over gx
    # which is used to calculate  gx_Norm[x] == gx / gx_Int[x]
    igx = gx.createIntegral(ROOT.RooArgSet(x))
    print "gx_Int[x] = ", igx.getVal()

    # I n t e g r a t e   n o r m a l i z e d   p d f   o v e r   s u b r a n g e
    # ----------------------------------------------------------------------------

    # Define a range named "signal" in x from -5,5
    x.setRange("signal", -5, 5)

    # Create an integral of gx_Norm[x] over x in range "signal"
    # ROOT.This is the fraction of of p.d.f. gx_Norm[x] which is in the
    # range named "signal"
    igx_sig = gx.createIntegral(ROOT.RooArgSet(x), ROOT.RooFit.NormSet(
        ROOT.RooArgSet(x)), ROOT.RooFit.Range("signal"))
    print "gx_Int[x|signal]_Norm[x] = ", igx_sig.getVal()

    # C o n s t r u c t   c u m u l a t i v e   d i s t r i b u t i o n   f u n c t i o n   f r o m   p d f
    # -----------------------------------------------------------------------------------------------------

    # Create the cumulative distribution function of gx
    # i.e. calculate Int[-10,x] gx(x') dx'
    gx_cdf = gx.createCdf(ROOT.RooArgSet(x))

    # Plot cdf of gx versus x
    frame = x.frame(ROOT.RooFit.Title("c.d.f of Gaussian p.d.f"))
    gx_cdf.plotOn(frame)

    # Draw plot on canvas
    c = ROOT.TCanvas("rf110_normintegration",
                     "rf110_normintegration", 600, 600)
    ROOT.gPad.SetLeftMargin(0.15)
    frame.GetYaxis().SetTitleOffset(1.6)
    frame.Draw()

    c.SaveAs("rf110_normintegration.png")

if __name__ == "__main__":
    rf110_normintegration()